Geometry Standard

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Instructional programs should enable all students to

- Analyze characteristics and properties of two-and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

Grades 6-8 Expectations: In grades 6-8 all students should -

  • precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties
  • understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects
  • create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Grade 9-12 Expectations: In grades 9-12 all students should -

  • analyze properties and determine attributes of two- and three-dimensional objects
  • explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them
  • establish th validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others
  • use trigonometric relationships to determine lengths and angle measures

- Specify locations and describe spatial relationships using coordinate geometry and other representational systems

Grade 6-8 Expectations: In grade 6-8 all students should-

  • use coordinate geometry to represent and examine the properties of geometric shapes
  • use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides

Grade 9-12 Expectations: In grade 9-12 all students should-

  • use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze geometric situations
  • investigate conjectures and solve problems involving two-and three-dimensional objects represented with Cartesian coordinates

- Apply transformations and use symmetry to analyze mathematical situations

Grade 6-8 Expectations: In grade 6-8 all students should-

  • describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling
  • examine the congruence, similarity, and line or rotational symmetry of objects using transformations

Grade 9-12 Expectations: In grade 9-12 all students should-

  • understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices
  • use various representations to help understand the effects of simple transformations and their compositions

- Use visualization, spatial reasoning, and geometric modeling to solve problems

Grade 6-8 Expectations: In grade 6-8 all students should-

  • draw geometric objects with specified properties, such as side lengths or angle measures
  • use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume
  • use visual tools such as networks to represent and solve problems
  • use geometric models to represent and explain numerical and algebraic relationships
  • recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life

Grade 9-12 Expectations: In grade 9-12 all students should-

  • draw and construct representations of two- and three-dimensional geometric objects using a variety of tools
  • visualize three-dimensional objects and spaces from different perspectives and analyze their cross sections
  • use vertex-edge graphs to model and solve problems
  • use geometric models to gain insights into, and answer questions in, other areas of mathematics
  • use geometric ideas to solve problems in, and gain insights into, other disciplines and other ares of interest such as art and architecture


2011 NCTM